Quantization of the cotangent bundle via the tangent groupoid

 Access to full text

 Full (PDF)

1. [1] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization, I and II. Annals of Physics 111 (1978), 61-110 and 111 (1978), 111-151. Zbl0377.53024
2. [2] J. F. Cariñena, J. Clemente-Gallardo, E. Follana, J. M. Gracia-Bondía, A. Rivero and J. C. Varilly, Connes' tangent groupoid and strict quantization, J. Geom. Phys. 32 (1999), 79-96. Zbl0961.53047
3. [3] J. Clemente-Gallardo, Ph. D Thesis, University of Zaragoza, 1999. 
4. [4] A. Connes, Noncommutative Geometry, Academic Press, London, 1994. 
5. [5] A. Connes and Hilson, Déformations, morphismes asymptotiques et K-théorie bivariante, C. R. Acad. Sci. Paris 311, Sér. I, 101-106. 
6. [6] M. De Wilde and P. B. Lecomte. Existence of star products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds. Lett. Math. Phys. 7 (1983), 487-496. Zbl0526.58023
7. [7] B. Fedosov, Deformation quantization and index theory, Akademie Verlag, 1996. 
8. [8] M. J. Gotay, Obstructions to quantization, preprint math-ph/9809011; The Juan Simo Memorial Volume, J. Marsden and S. Wiggins (eds.), Springer, 1998. 
9. [9] M. Hilsum and G. Skandalis, Morphismes K-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov, Ann. Sci. Ec. Norm. Sup. 20 (1987), 325-390. Zbl0656.57015
10. [10] N. P. Landsman, Strict deformation quantization of a particle in external gravitational and Yang-Mills fields, J. Geom. Phys. 12 (1993), 93-132. Zbl0789.58081
11. [11] S. Lang, Differential Manifolds, Addison-Wesley, Reading, Mass., 1972. 
12. [12] B. Monthubert and F. Pierrot, Indice analytique et groupoïdes de Lie, C. R. Acad. Sci. Paris 325 (1997), 193-198. Zbl0955.22004
13. [13] M. Rieffel, Questions on quantization, preprint quant-ph/9712009; Proc. Internat. Conf. on Operator Algebras and Operator Theory (Shanghai, 1997).